Lambda-compact operators as a surjective hull of certain nuclear operators

Abstract

In this master’s thesis we introduce nuclear operators defined by a triplet of sequence spaces extending both the (r; p; q)-nuclear operators of Pietsch [Pie80, Chapter 18] as well as lambda-nuclear operators of Ramanujan [Ram70]. This enables us to represent lambda-compact operators introduced by Bhar and Gupta [GB13] as the surjective hull of a certain quasi-Banach operator ideal (following the ideas of [ALO12] and [Pie14]). This, in particular, yields that lambda-compact operators themselves form a quasi-Banach operator ideal given some modest requirements on the sequence space lambda.